A fresco from the Villa Arianna, Boscoreale, on show at the British Museum's Life and Death in Pompeii and Herculaneum exhibition

"Let's jump off that bridge when we get to it," said Neil MacGregor, director of the British Museum, when pressed on the putative future of the institution were Scotland to become independent.

The question was raised at a British Museum press conference today not by a journalist, but, intriguingly, by Gus O'Donnell, cabinet secretary under three prime ministers and once the most powerful civil servant in the land.

Even so – after pointing out that his would be one of dozens of "British" institutions that would have to rethink if the union dissolved – MacGregor conceded that there would be a huge "existential question" for the museum, which was founded by act of parliament in 1753, were the vote to swing in favour of independence next year.

"It's a very serious question," said the Glaswegian. "The British Museum is the first cultural evidence of the union. It was part of the response to the events of 1745 – the first British thing created after that threat to the union – and it sent out a big statement. It was marrying Scottish Enlightenment ideas to the London's global contact, and it was a real expression of what that new country [Britain] was."

By way of comparison the British Council, for example, has said that whatever the outcome of the independence vote it will still support cultural projects from Scotland, such as its presence at the Venice Biennale.

The other side of the coin is how relevant the British Museum actually feels as a cultural expression in Glasgow, Inverness or Aberdeen – especially when Edinburgh has its own National Museum, albeit with a different focus from that of the Bloomsbury institution.

Is the post-Enlightenment Britishness of the London museum utterly out of synch with a fracturing, post-imperial world? Or is its new connectedness via the web and its vigorous commitment to national links beyond London (not least sending its Pharoah: King of Egypt exhibition to Kelvingrove) proving it to be as crucial as ever, in fact ever more so? All this is speculation for now, but if Scotland becomes independent it will, beyond a doubt, change the terms of engagement for the museum on both sides of the border.